Game theory: pure and mixed strategies
General · Mathematics
Study notes
Q: Find mixed Nash for matching pennies: [[1,-1],[-1,1]] (row player). No pure Nash (cycles!). Row mixes (p,1-p): column indifferent: p(1)+(1-p)(-1) = p(-1)+(1-p)(1). 2p-1 = 1-2p: p = 1/2. Similarly q = 1/2. Value: 0! Nash: (1/2,1/2): each indifferent! (Minimax: von Neumann!)